In this section we consider an operator \((E-\lambda A)^{-1},\)  where \(A:=R_{\tilde{W}}.\)  Note that absolutely analogously to the proof of Lemma 2
[1]} we can prove that \(\mathrm {P}(A)\in \mathbb {C}\setminus \mathfrak {L}_{0},\)  where \(\mathfrak {L}_{0}\)  is a sector containing the numerical range of the operator \(A.\)  It follows easily from this fact that the operator \((E-\lambda A)^{-1}\)  is defined on the Hilbert space \(\mathfrak {H}\)  when \(\lambda \in \mathbb {C}\setminus \mathfrak {L}_{0}.\)
